The extraction of principal components from images is well known, with one extraction technique using neural networks as described in U.S. Pat. No. 5,377,305. Principal components are those which have self-same characteristics or features from one section of an image to another. This self-same characteristic or feature is encoded in principal component tiles in which the image is first subdivided into rectilinear subsections or tiles. A transform is then applied to the tiles which results in a small number of principal component tiles. The dot product of the principal component tiles with the original image results in a set of weights which when transmitted with the principal component tile permits reconstruction of the image. Mathematically speaking the principal components are the basis of a matrix analysis where one is looking for orthogonal tiles ordered by energy.
Thus the original image is modeled through extraction of principal components. The modeling at least in one instance permits compression so that the transmission of the image can be accomplished on a reduced time scale.
By way of background, as to standard compression methods, first, there is the process of compaction. This is done for conventional applications by some suitable transformation which provides an initial compact representation. In the case of JPEG, for example, the discrete cosine transformation (DCT) provides compaction. Associated with each transformation is a basis. The bases may be of fixed scale as with the JPEG-DCT, or may vary in scale motivated by the prospect for very low bit rate transmission as with current wavelet techniques.
Up until recently, standard compression has not been thought suitable for principal component image modeling and compression, which can involve temporal and characteristics other than spatial characteristics. Standard compression methods such as JPEG or wavelet transforms focus only on the spatial characteristics of the image, with JPEG and wavelet transforms being described in U.S. Pat. Nos. 6,347,157; 6,343,155; 6,343,154; 6,229,926; 6,157,414; 6,249,614; 6,137,914; 6,292,591, and 6,298,162.
Standard image compression uses fixed bases. The results are good for standard imagery and are oriented to same. However, for more exotic imagery, e.g., hyperspectral imagery, there is a need for new modeling and compression techniques.
More specifically, in hyperspectral imagery the number of features used to characterized an image is multiplied. For instance, non-spatial features such as heat, hardness, texture, and color are often times used in image presentation. The fixed basis of JPEG and others cannot handle the expanded feature set associated with hyperspectral imagery. Nor can these techniques handle voxels which are used to encode numbers of additional features of an image. Transmission of voxel images is computationally intense and less computationally intense compression techniques are required for their transmission.
In the past, principal component analysis has been used to indicate what features or characteristics of an image are to be utilized in a compression process. Such characteristics can be spatial or temporal or indeed any of a wide variety of characteristics such as for instance color, heat, or other hyperspectral components. In order to achieve modeling or indeed compression, it is important to identify correlations in an image. How to do this in a computationally efficient manner and one which is universal across all platforms is a challenge.
By way of further background, there are currently two main compression techniques and both are dependent on fixed bases. One, the JPEG standard, is based on the DCT transform to provide compaction. The essence of this technique is based on two factors: the approximation of the Karhunen-Loeve (KL) transform by the DCT and the extent of the autocorrelation function which seems to optimize for most images to 8×8 tiles. Using these factors, the JPEG compression standard made a compromise decision omitting the use of scale. The initial DCT transform on 8×8 tiles provides compaction which is then further compressed using zigzag scanning followed by run length and Huffman coders. JPEG produces good images at moderate compression.
The other relevant technique is wavelet compression. Wavelet technology has challenged assumptions in the JPEG standard on several fronts. Most important, scale is implicit to wavelet techniques. Scale allows ordered extraction of fine and coarse features. Use of scale, from fine to coarse, means that subsequent decomposition will be on decimated image. As a result, wavelet decomposition which provides control over computation is limited by decimation. Each level has ¼ the points of the previous level so computation is about 1.33 N2k where k is the size of the wavelet filter and N is image size in one dimension. Second, wavelets are usually applied to images on a separable though fixed basis. Thus, wavelet decomposition is applied in the x and y dimensions separately. This seems to fit well with human visual perception which is oriented to horizontal and vertical detail. Two dimensional bases are implicit in this decomposition. Third, a particularly good scheme for quantizing wavelet coefficients, Zero Tree Encoding2, has significantly advanced the state of the art in wavelet image compression. The combination of scale, compaction and quantization made wavelets the likely candidate for future generation JPEG compression standards.